Using Rewriting Systems to Compute Left Kan Extensions and Induced Actions of Categories

✍ Scribed by Ronald Brown; Anne Heyworth

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 432 KB
• Volume: 29
• Category: Article
• ISSN: 0747-7171
• DOI: 10.1006/jsco.1999.0294

✦ Synopsis

The aim is to apply string-rewriting methods to compute left Kan extensions, or, equivalently, induced actions of monoids, categories, groups or groupoids. This allows rewriting methods to be applied to a greater range of situations and examples than before. The data for the rewriting is called a Kan extension presentation. The paper has its origins in earlier work by Carmody and Walters who gave an algorithm for computing left Kan extensions based on extending the Todd-Coxeter procedure, an algorithm only applicable when the induced action is finite. The current work, in contrast, gives information even when the induced action is infinite.